On the growth of torsion in the cohomology of arithmetic groups

Bergeron and Venkatesh give a precise conjecture about the growth of the order of the torsion subgroup of homology groups over a tower of cocompact congruence subgroups. In this talk, we describe our computational investigation of this phenomena. We consider the cohomology of several (non-cocompact) arithmetic groups, including GL_n(Z) for n = 3, 4, 5 and GL_2(O) for various rings of integers, and observe its growth as a function of level. In all cases where our dataset is sufficiently large, we observe excellent agreement with the same limit as in the predictions of Bergeron-Venkatesh. This is joint work with Avner Ash, Paul Gunnells, and Mark McConnell.